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Title: Weakly informative priors and prior-data conflict checking for likelihood-free inference Authors:  Atlanta Chakraborty - National University of Singapore (Singapore)
David Nott - National University of Singapore (Singapore) [presenting]
Michael Evans - University of Toronto (Canada)
Abstract: Bayesian likelihood-free inference, which is used to perform Bayesian inference when the likelihood is intractable, enjoys an increasing number of important scientific applications. However, many aspects of a Bayesian analysis become more challenging in the likelihood-free setting. One example of this is prior-data conflict checking, where the goal is to assess whether the information in the data and the prior are inconsistent. We consider methods for prior-data conflict checking, which are applicable regardless of whether the likelihood is tractable or not. In constructing our checks, we consider checking statistics based on prior-to-posterior Kullback-Leibler divergences. The checks are implemented using mixture approximations to the posterior distribution and closed-form approximations to Kullback-Leibler divergences for mixtures, which make Monte Carlo approximation of reference distributions for calibration computationally feasible. When prior-data conflicts occur, it is useful to consider weakly informative prior specifications in alternative analyses as part of a sensitivity analysis. As the main application of our methodology, we develop a technique for searching for weakly informative priors in likelihood-free inference, where the notion of a weakly informative prior is formalized using prior-data conflict checks.